中文摘要：

讨论了带有Carreau型黏性的非牛顿流体非凸守恒律方程Cauchy问题冲击波解的渐近稳定性。在小扰动情况下,运用单调算子理论以及加权能量估计方法,证明了该类黏性非凸守恒律方程的黏性冲击波解是渐近稳定的,这一结果对冲击波的强度没有限制条件。

英文摘要：

The asymptotic stability of the shock wave solutions to the Cauchy problem for viscosity non-convex conservation laws of the Carreau type is discussed. In the case of small perturbations, the monotone operator theory and the weighted energy estimation method are used to prove that the viscous shock wave solutions of this kind of viscous non-convex conservation law equation are asymptotically stable, and this result is not affected by the strength of the shock wave.